An application of Carlitz's formula

In this note we establish a new transformation formula for the generalized hypergeometric function of two variables. On specializing its parameters, it yields the interesting result:

${}_4\text{F}{}_3\text{γ2β?γ1+}\text{1}\text{2}\text{α,}\text{1}\text{2}\text{+}\text{1}\text{2}\text{α;1}\text{1}\text{2}\text{(1+2β),2+α,1+β;}\text{=}\text{βΓ(2β)Γ(2β?α?γγ)}\text{(β?γ)Γ(2β?α)Γ(2β?γ)}$

. valid for Rl(2β ? α ? γ) > 0. When γ = ?n (a negative integer), it reduces to a result due to Professor Carlitz. Several other new summation formulae for ₅F₄(1), ₄F₃(1) and for the hypergeometric function of two variables are obtained.     

Spectroscopic study of 2-, 4- and 5-substituents on pKa values of imidazole heterocycles prone to intramolecular proton-electrons transfer

New 2-(1H-imidazol-2-yl)phenols (L1Et–L8tBuPt) bearing a phenolic proton in the vicinity of the imidazole base were prepared and characterized. Experimental studies of the dependence of their protonation/deprotonation equilibrium on substituent identities and intramolecular hydrogen bonding tendencies were carried out using electronic absorption spectroscopy at varying pH values. In order to make comparison, 2-(anthracen-10-yl)-4,5-diphenyl-1H-imidazole (L9Anthr) bearing no phenolic proton and 4,5-diphenyl-2-(4,5-diphenyl-1H-imidazol-2-yl)-1H-imidazole (L10BisIm) bearing two symmetrical imidazole base fragments were also prepared and experimentally investigated. DFT calculations were carried out to study frontier orbitals of the investigated molecules. While electron-releasing substituents produced increase in protonation–deprotonation pK_as for the hydroxyl group, values for the imidazole base were mainly affected by polarization of the imidazole ring aromaticity across the 2-imidazole carbon and the 4,5-imidazole carbons axis of the imidazole ring. It was concluded that electron-releasing substituents on the phenol ring and/or electron-withdrawing substituents on 4,5-imidazole carbons negatively affects donor strengths/coordination chemistries of 2-(1H-imidazol-2-yl)phenols, and vice versa. Change of substituents on the phenol ring significantly altered the donor strength of the imidazole base. The understanding of pK_a variation on account of electronic effects of substituents in this work should aid the understanding of biochemical properties and substituent environments of imidazole-containing biomacromolecules.     

Development and analysis of a malaria transmission mathematical model with seasonal mosquito life-history traits

In this paper, we develop and analyze a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission, and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation system. We provide a global analysis of the model depending on two threshold parameters and (with ). When , then the disease-free stationary state is locally asymptotically stable. In the presence of the human disease-induced mortality, the global stability of the disease-free stationary state is guarantied when . On the contrary, if , the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a sub-critical (backward) bifurcation is possible at . Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa.     

A novel anticancer diterpenoid from Jatropha gossypifolia

Jatropha gossypifolia root bark is used in ethnomedicine for bacterial infections and cancer of the lungs. Phytochemical investigation resulted in the isolation and characterization of a potent anticancer and novel lathyrane diterpenoid compound, abiodone, with an unusual methylene group. The structure of this novel compound was established by 1D, and 2D NMR spectroscopic experiments a nd confirmed by X-ray analysis.     

Analytical Evaluation of Carbamate and Organophosphate Pesticides in Human and Environmental Matrices: A Review

Pesticides are synthetic compounds that may become environmental contaminants through their use and application. The high productivity achieved in the agricultural industry can be credited to the use and application of pesticides by way of pest and insect control. As much as pesticides have a positive impact on the agricultural industry, some disadvantages come with their application in the environment because they are intentionally toxic, and this is more towards non-target organisms. They are grouped into chlorophenols, organochlorines, synthetic pyrethroid, carbamates, and organophosphorus based on their structure. The symptoms of exposure to carbamate (CM) and organophosphates (OP) are similar, although poisoning from CM is of a shorter duration. The analytical evaluation of carbamate and organophosphate pesticides in human and environmental matrices are reviewed using suitable extraction and analytical methods.     

Slow magnetic relaxation in mononuclear tetrahedral cobalt(II) complexes with 2-(1H-imidazol-2-yl)phenol based ligands

Three mononuclear cobalt(II) complexes based on the 2-(4,5-diphenyl-1H-imidazol-2-yl)phenol ligand and its nitro and methoxy derivatives have been synthesized and investigated. For two of these complexes, which were derived from the parent ligand and its nitro derivative, the molecular structures have been determined by X-ray crystallography. A distorted tetrahedral coordination environment is observed for the cobalt(II) centers with two bidentate N,O ligands. The magnetic properties have been studied by susceptibility and magnetization measurements revealing the presence of high-spin cobalt(II) ions with a considerable zero-field splitting in the order of D = –35 to –41 cm⁻¹ for the three complexes. With an applied dc field the ac susceptibility data reveal a slow magnetic relaxation which is characteristic for single-molecular magnet (SMM) behavior.     

Regioselective Synthesis of Pyrazoles and Isoxazoles with Cyclopropanated Side‐Chain

Pyrazoles and isoxazoles with cyclopropanated side‐chain were prepared by cyclization of cyclopropanated 1,3,5‐tricarbonyl compounds with hydrazine and hydroxylamine, respectively. The regioselectivity is influenced by the reaction conditions.     

Couple stress fluid flow with variable properties: A second law analysis

The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge‐Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity variation parameter, and Grashof number. The study is relevant to lubrication theory.